The most abundantly available genetic markers in the mammalian genomes are single nucleotide polymorphisms (SNPs), and these subtle genetic variations can be either neutral genetic landmarks or detrimental genetic changes resulting in transcriptional dysregulations or protein function abnormalities. Alleles at closely linked SNPs tend to travel together when passed from generation to generation, and this phenomenon has been known as linkage disequilibrium (LD). The allele configuration of an ordered list of linked loci on one chromosome is known as a haplotype. Distinctive patterns of haplotypes reveal distinctive population histories, and the delineation of a dense genome-scale SNP map by the International HapMap project promises to provide the research community with a reference grid of markers for identifying common haplotypes of haplotype blocks that underlie genetic susceptibility to common human diseases. This will greatly enhance our ability in developing novel disease diagnostic procedures and individualized therapies. However, as the accumulation of SNP genotype data accelerates over the past few years in both public and private sections, tools for determining haplotype phases, for LD analysis, and for uncovering epistatic interactions remain a bottleneck towards the systematic understanding and analysis of the SNP variation of the human genetic diseases. The general goal of this research is to advance our capability in analyzing and understanding the data resulting from the HapMap project and various genetic epidemiology studies that take advantage of the dense genetic map produced by the HapMap project. More specifically, we aim to (a) develop more robust and accurate algorithms for inferring haplotype phases from genotype information, which can take into consideration the evolutionary relationship among the sampled individuals; (b) design, test, and apply novel statistical models and computational strategies for fine-mapping genetic mutations that interact to cause diseases; and (c) develop, implement, and apply novel statistical model based algorithms to detect gene-gene and gene-environment interactions in whole-genome association studies. These tasks are particularly urgent because, to a large degree, nowadays we are limited more by our ability in utilizing, organizing, and understanding relevant genetic data than by generating them. By developing effective algorithms for haplotype determination, SNP selection, LD-based fine mapping, gene-gene interaction predictions, and gene-environment interactions in whole genome association studies, tremendous strides can be made in our understanding of the genetic basis of complex human traits. [unreadable] [unreadable] [unreadable]